document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=467372>Question 467372</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If x + y is 4 more than x - y which of the following statements must be true?\r<BR>\n" );
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document.write( "I. x = 2<BR>\n" );
document.write( "II. y = 2<BR>\n" );
document.write( "III. xy has more than one value\r<BR>\n" );
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document.write( "A) I only<BR>\n" );
document.write( "B) II only<BR>\n" );
document.write( "C) III only<BR>\n" );
document.write( "D) I and III only<BR>\n" );
document.write( "E) II and III only\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #320670 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=320670\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the way I see it, selections I, II, and III are all true.<BR>\n" );
document.write( "that does not appears to be one of the possible answers though.<BR>\n" );
document.write( "the answer to the problem is that y = 2 and x can be any value.<BR>\n" );
document.write( "selection I says that x = 2. <BR>\n" );
document.write( "this is true, but it doesn't state that x can also be any other value, so this statement has to be false, or at least misleading.<BR>\n" );
document.write( "selection II says that y = 2.  <BR>\n" );
document.write( "this is true.  <BR>\n" );
document.write( "y has to be equal to 2.<BR>\n" );
document.write( "no other value of 2 will satisfy the equation.<BR>\n" );
document.write( "selection III says that x * y has more than one value.<BR>\n" );
document.write( "this is also true.<BR>\n" );
document.write( "y has to be equal to 2 but x can be any value so the product of x and y can have multiple values depending on the value of x.<BR>\n" );
document.write( "i would say your answer has to be E) II and III only.<BR>\n" );
document.write( "even though I is also true, it is not completely true so, if i had to pick one of the answers to discard, it would have to be I.<BR>\n" );
document.write( "by the way:<BR>\n" );
document.write( "the equation resulting from your problem statement is:<BR>\n" );
document.write( "x + y = x - y + 4<BR>\n" );
document.write( "add y to both sides of this equation and you get:<BR>\n" );
document.write( "x + 2y = x + 4<BR>\n" );
document.write( "subtract x from both sides of this equation and you get:<BR>\n" );
document.write( "2y = 4<BR>\n" );
document.write( "divide both sides of this equation by 2 and you get:<BR>\n" );
document.write( "y = 2<BR>\n" );
document.write( "that's the solution for y.<BR>\n" );
document.write( "substituting for y in the original equation gets you:<BR>\n" );
document.write( "x + y = x - y + 4 becomes:<BR>\n" );
document.write( "x + 2 = x - 2 + 4 which becomes:<BR>\n" );
document.write( "x + 2 = x + 2<BR>\n" );
document.write( "subtract 2 from both sides of this equation and you get:<BR>\n" );
document.write( "x = x<BR>\n" );
document.write( "that's an identity equation which means that x can be any value.<BR>\n" );
document.write( "subtract x from both sides of the equation and you get:<BR>\n" );
document.write( "0 = 0<BR>\n" );
document.write( "x disappears and the equation is true.<BR>\n" );
document.write( "that's another indication that x can be any value and the original equation will be true.<BR>\n" );
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